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Since i ‘ve recently had a couple of university professors analyze the expectations augmented Phillips curve, I ‘d like to do a short analysis of the relationship, especially in the context of inflation targeting by central banks. First, it is important to point out that the original Phillips equation reflected a relationship between wage growth and unemployment. The modern Phillips curve assumes constant real wages in order to substitute wage inflation for the inflation rate and come up with:

π = π* – ε(u – u*) where π* is the expected inflation rate and u* is the natural rate of unemployment.

This assumption shows its weakness if one uses another route to come up with a breakdown of inflationary sources. Using the equation of exchange:

PQ = PY (Q: real output, Y: real income)

and noting that income is distributed between wages and profits we can come up with:

PQ = (W + U)

Multiplying and dividing by W:

PQ = (W + U/W) * W

W + U/W is actually the aggregate mark-up of profits to wages, which can be set to m:

PQ = mW

Dividing both parts by L (employment):

P*(Q/L) = m*(W/L)

and renaming Q/L to average labor productivity (APL) and W/L to the money wage and taking natural logs we end up with:

π = m + w – APL

In other words, inflation is created by the excess increase of wages and markups to the growth of productivity. Given that the original Phillips curve focused on wage inflation, we can substitute w with the expectations augmented equation to reach:

π = m + (π* – ε(u – u*)) – APL

and moving inflation expectations to the left:

π – π* = m – APL – ε(u – u*)

Modern central banks follow inflation targeting with a view of minimizing the output gap. Taking that policy as given and assuming it is successful at anchoring actual inflation to the expected it is clear that:

m – APL = ε(u – u*)

As a result, only if the markup growth rate is equal to the increase of labor productivity will the outcome be unemployment close to the natural rate while workers will enjoy constant real wages. If firms manage to increase their markups more than productivity they will be able to earn a larger share of income while leading the economy to an unemployment gap. The increased unemployment will lower labor bargaining power and its ability to achieve wage increases. Consequently, pure inflation targeting will not necessarily lead to an optimal outcome but can allow ‘capitalists’ (used with the classical definition of owners of the means of production) to secure higher shares of income while lowering the labor force negotiating power and increasing the unemployment gap. Coupled with a financial sector willing to provide easy credit, this policy can have long-term redistributional effects.

* The original discussion appeared on heteconomist.